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An energy approach is proposed to describe the electromigration induced grain rotation under high current density. The driving force is assumed to arise from the grain-boundary energy reduction and increase of the inner energy from the joule heating. Energy dissipates by the grain boundary diffusion under electromigration and viscous boundary sliding is considered. Based on the conservation of energy production and dissipation, an equilibrium equation is developed to predict the grain rotation rate analytically. It is recognized that the grain rotates with the reducing of electrical resistivity and inversely proportional to the grain length. The theoretical prediction is compared with the experimental data, which shows good accuracy on the rotation trend and the specific rotation rate. Keywords: Electromigration, Grain rotation, Energy, Analytical model